HW 06

The Quarto template for this assignment may be found in the repository at the following link: https://classroom.github.com/a/lry1jv5e

The "Bechdel test" is a test for movies that examines gender stereotypes as represented in film. To successfully pass the Bechdel test, a film must feature at least two named female-identifying characters that have a conversation about a topic other than a man. Today's data represent approximately 1,500 films for which the Bechdel test was applied.

The variables in the dataset are as follows:

• year: the year in which the movie came out
• title: the title of the film
• binary: whether the film passed (PASS) or failed (FAIL) the Bechdel test
• budget_2013: the budget of the film, inflation-adjusted to 2013 dollars
• rated: whether the film was rated PG, PG-13, or R by the MPAA
• runtime: the runtime of the film in minutes
• imdb_rating: the IMDB rating of the movie (a scale from 0 - 10)

All interpretations must be in terms of odds ratios unless otherwise specified.
1. Fit a logistic regression model that predicts whether a film passes the Bechdel test using MPAA rating, runtime, and IMDB rating. Interpret each of the slope coefficients. Consider passing the Bechdel test as a "success" (the event of interest).
2. Consider two 90 minute movies that are both rated PG-13. What are the odds ratio and risk ratio for passing the Bechdel test if one of the movies has an IMDB rating of 1 and another has an IMDB rating of 2? What about for two 90 minute movies that are rated PG-13 if one of the movies has an IMDB rating of 9 and another has an IMDB rating of 10?
3. Evaluate whether the linearity assumption is satisfied for the continuous predictors in the model.
4. Suppose you use your logistic regression model as a classifier for passing the Bechdel test by using a threshold of 0.5 predicted probability (that is, predicted probabilities for passing the test above 0.5 are classified as “passing”). What are the sensitivity, specificity, positive predicted value, and negative predicted value of your classifier among these movies?
5. Construct an ROC curve for your classifier using this model. What AUC do you achieve?